Harrison will oversee the consultancy's public affairs offering and co-ordinate business development opportunities across sectors and geographies.
She co-founded public affairs business Blueprint in 2003, which joined a firm called FD that later became part of FTI Consulting.
Harrison, who has led the Brussels practice for the past decade, will continue to be based in Belgium's capital.
Senior managing director Hans Hack, pictured below, will succeed her as head of the Brussels office.
He has been part of the Brussels leadership team for six years, running day-to-day operations for the past year.
"Political and business issues increasingly span borders, so now is the right time for us to combine our expertise at a global level, with Julia stepping up to lead our public affairs offering," said Mark McCall, global segment leader of FTI's strategic communications segment.
"Julia has the experience, credibility and track record to make sure we go beyond this and deliver a consistent global point of view and quality of service to clients. This is an important and valuable element of our business."
Harrison added: "I'm delighted to be taking on this global public affairs role, which is a significant driver of our business; indeed, the practice has nearly doubled in size since 2013. Clients want to work with the best people, and we have a world-class team.
"This is a great opportunity to work with all the experts we have in place across the world, pulling together an offering that is a real differentiator when it comes to clients and business development — no matter where they need that support or in what sector."